Well-Posed Gaussian-Like Models for Image Denoising and Sharpening

It is well-known that Gaussian filter is the most important model in image denoising. However, the inverse of the Gaussian model for image sharpening is seriously ill-posed. In this paper, we propose several variations of the Gaussian model, which are derived from the varied diffusion equations. Explicit forms for these models (filters) are given in the Fourier space, which facilitate the usage of these models in the image processing. Each of the proposed models has its own distinct feature and plays the role of the image denoising as the Gaussian filter. Furthermore, the inverse problem of the varied diffusion equations are well-posed. Some image denoising and sharpening experiments are conducted showing that the modified models yield more desirable results.